Nuprl Lemma : subtype-iff-id-mem-fun
∀[A,B:Type]. uiff(A ⊆r B;λx.x ∈ A ⟶ B)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
equal-wf-base,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaEquality,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalHypSubstitution,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
functionEquality,
baseClosed,
because_Cache,
productElimination,
independent_pairEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. uiff(A \msubseteq{}r B;\mlambda{}x.x \mmember{} A {}\mrightarrow{} B)
Date html generated:
2016_05_13-PM-04_14_14
Last ObjectModification:
2016_01_14-PM-07_28_45
Theory : subtype_1
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